Answer:
[tex]Suppose~that~two~numbers~are~x~and~y.\\From~the~first~condition,\\x+y=4.........(1)\\or, y=4-x.......(2)\\From~the~second~condition,\\x^2+y^2-3xy=76\\or, (x+y)^2-2xy-3xy=76\\or, 4^2-5xy=76\\or, -5xy = 76-16\\or, -5xy = 60\\or, xy = -12\\From~eq^n~(2),\\x(4-x)=-12\\or, 4x-x^2=-12\\or, x^2-4x-12=0\\or, x^2 +2x-6x-12=0\\or, x(x+2)-6(x+2) = 0\\or,(x+2)(x-6) = 0\\i.e. x = -2 ~or ~6\\When~ x=-2, y=4-(-2) = 4+2 =6\\When~x=6, y=4-6 = 4-6 = -2\\So,~the~two~numbers~are~-2~and~6.[/tex]
Answer:
-2 and 6
Step-by-step explanation:
Mark the first number as x
and the second number as y
Since x + y = 4
y = 4 - x
// substitute the given value of y into the equation
[tex]x^{2} + y^{2}[/tex] - 3xy = 76
[tex]x^{2}[/tex] + [tex](4-x)^{2}[/tex] - 3 * x * (4 - x) = 76
[tex]x^{2}[/tex] + 16 - 8x + [tex]x^{2}[/tex] - 12x + 3[tex]x^{2}[/tex] = 76
[tex]x^{2}[/tex] + [tex]x^{2}[/tex] + 3[tex]x^{2}[/tex] - 20x = 76 - 16
5[tex]x^{2}[/tex] - 20x = 60
5[tex]x^{2}[/tex] - 20x - 60 = 0
// divide both sides by 5
[tex]x^{2}[/tex] - 4x - 12 = 0
// write -4 x as a difference, this way it is faster than calculating discriminant
[tex]x^{2}[/tex] + 2x - 6x - 12 = 0
// factor out x and -6 from the expression
x (x +2) - 6 (x +2) = 0
(x - 6) * (x + 2) = 0
// there are two possible cases
1) x - 6 = 0
2) x + 2 = 0
1) x = -2
2) x = 6
// substitute the given value of x into the equation
1) y = 4 - x = 4 - (-2) = 6
2) y = 4 - x = 4 - 6 = -2
Now we get two pairs (-2; 6) and (6; -2), which are the solutions to the system
Since their sequence as the question suggests is irrelevant, the numbers are -2 and 6
when calculating present value, the _____ the interest rate, the smaller the present value amount.
•smaller
•larger
when calculating present value, the _____ interest rate, the smaller the present value amount.
* smaller
* larger,✓
The correct value is,
''When calculating present value, the smaller the interest rate, the smaller the present value amount.''
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
To calculating the present value, The smaller the present value.
Now,
The correct value is,
''When calculating present value, the smaller the interest rate, the smaller the present value amount.''
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Can someone help me please?
Given:
A line segment AB.
A point is [tex]\dfrac{3}{10}[/tex] of the way from A to B.
To find:
The coordinates of that point.
Solution:
Section formula: If a point divide a line segment in m:n, then
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
From the given figure, it is clear that the two end points of the line segment are A(-4,-5) and B(12,4).
Let the unknown point be P. The point is [tex]\dfrac{3}{10}[/tex] of the way from A to B. It means,
[tex]\dfrac{AP}{AB}=\dfrac{3}{10}[/tex]
Let AP and AB are 3x and 10x, then
[tex]\dfrac{AP}{PB}=\dfrac{AP}{AB-AP}[/tex]
[tex]\dfrac{AP}{PB}=\dfrac{3x}{10x-3x}[/tex]
[tex]\dfrac{AP}{PB}=\dfrac{3x}{7x}[/tex]
[tex]\dfrac{AP}{PB}=\dfrac{3}{7}[/tex]
It means, point P divided the line segment in 3:7.
Using section formula, we get
[tex]P=\left(\dfrac{3(12)+7(-4)}{3+7},\dfrac{3(4)+7(-5)}{3+7}\right)[/tex]
[tex]P=\left(\dfrac{36-28}{10},\dfrac{12-35}{10}\right)[/tex]
[tex]P=\left(\dfrac{8}{10},\dfrac{-23}{10}\right)[/tex]
[tex]P=\left(0.8,-2.3\right)[/tex]
Therefore, the coordinates of the required point are (0.8, -2.3).
Classify the following triangle. Check all that apply.
Answer:
B & F
Step-by-step explanation:
Answer:
Right
Isosceles
But that’s all I got
Step-by-step explanation:
Find (x + 4)(x2 + x - 2). Write your answer in standard form.
Answer please
Answer:
X^3 + 5x^2 + 2x - 8
Step-by-step explanation:
Raina picks 20 flowers
1/4 are roses 2/5
are daisies
How many flowes are lilies?
Answer:
7 of the flowers were lilies.
Step-by-step explanation:
8 daises and 5 roses were picked. 8 + 5 = 13 20 - 13 = 7
7 of the flowers were lilies
Please help math 1-2 high school solving proofs.
Answer:
1= A
2= C
Step-by-step explanation:
I think this is right I'm not sure but I think it is.
hope this helps :)
find the product of 1x6x6
Answer:
36
Step-by-step explanation:
1x6=6
6x6=36
Hope this helps! :)
What are verbs? Example
Answer:
Hi! Hope this helps!
Step-by-step explanation:
A verb is used to describe actions.
Example: I JUMPED over the rock. In this sentence the verb is JUMPED
a ver
Step-by-step explanation:
a verb is a word used to describe an action , state , occurrence and forming the main part of a predicate of a sentence
ABCD is a parallelogram. If m/CDA = 63, then m/ABC = ? . The diagram is not to scale
it’s 63 because the sides are equal on both sides
At the city museum, child admission is $6.40 and adult admission is $9.90. On Saturday, twice as many adult tickets as child tickets were sold, for a total sales of $733.60. How many child tickets were sold that day?
Answer:
x child tickets, y adult tickets
6.40x+9.50y=1260.70
x+y=150
64x+95y=12607
x+y=150
If you solve this, you have to get x=53, y= 97.
So 53 child tickets and 97 adult tickets
HELPPPPPP ANYBODY KNOW????
] 8 Which expression is equivalent to 12x + 3y - 9x ?
А. 3x + Зу
В. бxy
С. 12х – бу
D. x+y
on a nice day there are 90% of children playing outside during recess. if there are 150 children how many of them are playing outside
Answer:
150.9 ?
Step-by-step explanation:
Please I need help ASAP
Answer:
It's 28!
Step-by-step explanation:
Answer:
28 in
Step-by-step explanation:
convert the whole thing to inches
5ft 8in = 68 in
8ft = 96 in
96-68 = 28 in
Write as an expression and solve (show your work!).
One-fourth the difference between twenty-one and five
Answer:
4
Step-by-step explanation:
1 / 4 x (21 - 5) =
1/4 x 16 = 4
Hope that helps!
Pick the similar triangles
someone help what the answer
Solve the following proportion: x 65 thousand
---- =. ------------
10 million. 40 million
Express your answer as a value written in standard form.
Answer:
2600000000000000000000000000000000000
Step-by-step explanation:
65 thousand times 40 million times 10 million
Answer:
great question
Step-by-step explanation:
Question 3
1 pts
• A solar panel absorbs 6,771 J of radiant energy, and produces 3,291 ) of
electrical energy. What is it's percent efficiency?
(make sure you multiply x100 to get a % between 0 and 100)
9514 1404 393
Answer:
48.6%
Step-by-step explanation:
Efficiency of energy conversion is the quotient of output energy and input energy.
(3291 J)/(6771 J) × 100% ≈ 48.6%
The solar panel's conversion efficiency is about 48.6%.
_____
Additional comment
With current (2021) technology, the best efficiency one can expect from a solar panel is in the neighborhood of 23%.
To the nearest inch, a door is 75 in. tall and 35 in. wide. What is the ratio of the
width to the height?
Answer:
35 in to 75in
Step-by-step explanation:
One year Hank had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.36 . Also, Jane had the lowest ERA of any female pitcher at the school with an ERA of 3.49 . For the males, the mean ERA was 4.449 and the standard deviation was 0.792 . For the females, the mean ERA was 5.091 and the standard deviation was 0.669 . Find their respective z-scores. Which player had the better year relative to their peers, Hank or Jane
Answer:
Hank had a z-score of -1.375.
Jane had a z-score of -2.39.
Jane had the better year relative to their peers, due to her lower z-score.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Hank:
ERA of 3.36. For the males, the mean ERA was 4.449 and the standard deviation was 0.792. This means that we have to find Z when [tex]X = 3.36, \mu = 4.449, \sigma = 0.792[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.36 - 4.449}{0.792}[/tex]
[tex]Z = -1.375[/tex]
Hank had a z-score of -1.375.
Jane
ERA of 3.49. For the females, the mean ERA was 5.091 and the standard deviation was 0.669. This means that we have to find Z when [tex]X = 3.49, \mu = 5.091, \sigma = 0.669[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.49 - 5.091}{0.669}[/tex]
[tex]Z = -2.39[/tex]
Jane had a z-score of -2.39.
Which player had the better year relative to their peers, Hank or Jane
Low ERA is good, high is bad. This means that whoever had the lower z-score had the better year, and in this case, it's Jane
If the probability of having rain tomorrow is 60%, what is the probability of not having rain tomorrow?
The paved area is a square with sides 2 m long.
The paving stones for this area are squares that measure 50 cm by 50 cm
How many paving stones are needed?
Answer:
Step-by-step explanation:
2 meters = 200 cm
200 cm × (1 block)/(50 cm) = 4 blocks
4 blocks by 4 blocks = 16 blocks
Answer:
16 paving stones
Step-by-step explanation:
1 m = 100 cm
The square has sides 200 cm long
Its area is 200(200) = 40000 sq cm
Each paving stone has an area of 50(50) = 2500 sq cm
So 40000/2500 = 16 paving stones
1. An airplane flies with a constant
speed of 740 miles per hour. How
far can it travel in 2 hours?
Answer:
740×2= 1480 in 2 hours
hope this helps :)
a store charges 32% extra for credit items. if the cash price is $1100, what is the credit price?
Answer:
$1452
Step-by-step explanation:
[tex]CP=1100*1.32=$1452[/tex]
find the value of 2xy+3yz-xyz, when x=2, y=-2, z=4
Answer:
-16
Step-by-step explanation:
2xy + 3yz - xyz
x = 2, y = -2, z = 4
First, plug these values into the equation.
2(2)(-2) + 3(-2)(4) - (2)(-2)(4) = ?
Next, multiply the parentheses.
(-8) + (-24) - (-16) = ?
When you add a negative, you are actually subtracting the number. And when you subtract a negative, you are actually adding the number. Apply this to the equation.
-8 - 24 + 16 = ?
Now, simplify from left to right.
-32 + 16
-16
Your answer is -16.
Hope this helps!
When you stand on snow, the average pressure P (in pounds per square inch) that you exert on the snow varies inversely with the total area A (in square inches) of the soles of your footwear. Suppose the pressure is 0.43 pound per square inch when you wear the snowshoes shown. Write an equation that gives P as a function of A. Then find the pressure if you wear the boots shown. (A=400in^2)
Find the pressure if you wear the boots shown below. (A=60in^2)
Answer:
0.43*0.43
Step-by-step explanation:
The pressure on the snow if the area of the footwear is 400 in² is 0.0645 pounds per square inch.
What is pressure?The force applied perpendicular to an object's surface per unit area across which that force is spread is known as pressure.
[tex]P= \dfrac{W}{A}[/tex]
As it is given that the pressure is inversely proportional to the area of the footwear. Therefore, the relation can be written as,
[tex]P\propto \dfrac{1}{A}\\[/tex]
Now, introducing a constant to remove the proportionality symbol, w that is the weight of the person, therefore,
[tex]P= \dfrac{W}{A}[/tex]
Now, as the area of the shoe is 60in², the pressure on the snow is 0.43 pounds per square inch. Therefore, the value of w can be written as,
[tex]0.43= \dfrac{W}{60}\\\\W = 25.8\rm\ pounds[/tex]
Now, the pressure on the snow if the area of the footwear is 400 in².
[tex]P= \dfrac{W}{A}\\\\P= \dfrac{25.8}{400}\\\\P = 0.0645 \rm\ pounds\ per\ inch^2[/tex]
Hence, the pressure on the snow if the area of the footwear is 400 in² is 0.0645 pounds per square inch.
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Given the sequence −2,−8/3,−103,−4,−14/3,... find the recursive formula.
A. a1=−2 and an+1=an+5/3
B. a1=−2 and an+1=an+1/3
C. a1=−2 and an+1=an−2/3
D. a1=−2 and an+1=an−5/3
I suppose the third term should say -10/3, not -103.
Notice that
-2 = -6/3
-4 = -12/3
so that, starting with the first term a(1) = -6/3, the every following term is obtained by subtracting 2/3.
-2 - 2/3 = -6/3 - 2/3 = -8/3
-8/3 - 2/3 = -10/3
-10/3 - 2/3 = -12/3 = -4
and so on.
So the recursive rule is
a(1) = -2,
a(n + 1) = a(n) - 2/3, for n ≥ 1
or C.
The Harris Poll tracks the favorite sport of Americans who follow at least one sport. Results of the poll show that professional football is the favorite sport of 33% of Americans who folllow at least one sport, followed by baseball at 15%, mens college football at 10%, auto racing at 6%, mens professional basketball at 5%, and ice hockey at 5%, with other sports at 26%. Consider a survey in which 344 college undergraduates who follow at least one sport were asked to identify their favorite sport produced the following results:
Professional Football Baseball Men's college football Auto racing Men's professional basketball IceHockey OtherSports
111 39 46 14 6 20 108
Do college undergraduates students differ from the general public with regard to their favorite sports? Use x= .05.
Answer:
The calculated χ² = 20.779 falls in the critical region χ² ≥ 14.46 so we accept the null hypothesis that all the means are equal and college undergraduates students do not differ from the general public with regard to their favorite sports.
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0: the college undergraduates students do not differ from the general public with regard to their favorite sport
H0: μ1= μ2=μ3=μ4= μ5=μ6=μ7=μ
against the claim
Ha: the college undergraduates students differ from the general public with regard to their favorite sport
2) The significance level alpha is set at 0.05
3) The test statistic under H0 is ( Pearson goodness of fit test )
χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency
which has an approximate chi square distribution with 6 (n-1) d.f
4) Computations:
Under H0 , the observed frequencies are :
Observed Expected (O-E) (O-E)² (O-E)²/E
111 (0.33*344)=
113.52 -2.52 6.3054 0.0555
39 51.6 -12.6 158.76 3.0767
46 34.4 11.6 134.56 3.911
14 20.64 -6.64 44.0896 2.136
6 17.2 -11.2 125.44 7.293
20 17.2 2.8 7.84 0.4558
108 89.44 18.56 344. 4736 3.8514
344 20.779
5) The critical region is χ² ≥ χ² (0.025)6 = 14.45
6) Conclusion:
The calculated χ² = 20.779 falls in the critical region χ² ≥ 14.46 so we reject the null hypothesis that all the means are equal and college undergraduates students do not differ from the general public with regard to their favorite sports.
Given that all the results are lower or higher in percentage, but they do not exceed the 5.5% threshold, it can be said that college undergraduates students do not differ from the general public with regard to their favorite sports.
Since the Harris Poll tracks the favorite sport of Americans who follow at least one sport, and results of the poll show that professional football is the favorite sport of 33% of Americans who folllow at least one sport, followed by baseball at 15%, mens college football at 10%, auto racing at 6%, mens professional basketball at 5%, and ice hockey at 5%, with other sports at 26%, considering a survey in which 344 college undergraduates who follow at least one sport were asked to identify their favorite sport produced the following results:
Professional Football = 111 Baseball = 39 Men's college football = 46 Auto racing = 14 Men's professional basketball = 6 Ice Hockey = 20 Other Sports = 108
To determine if college undergraduates students differ from the general public with regard to their favorite sports, the following calculation must be performed:
Pro football = 111/344 = 0.3226 = 32.26% (-0.74). Baseball = 39/344 = 0.1133 = 11.33% (-3.67). Men's college football = 46/344 = 0.1337 = 13.37% (+3.37). Auto racing = 14/344 = 0.0406 = 4.06% (-2.94). Men's professional basketball = 6/344 = 0.0174 = 1.74% (-3.26). Ice Hockey = 20/344 = 0.0581 = 5.81% (+0.81). Other Sports = 108/344 = 0.3139 = 31.39% (+5.39).
Therefore, given that all the results are lower or higher in percentage, but they do not exceed the 5.5% threshold, it can be said that college undergraduates students do not differ from the general public with regard to their favorite sports.
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Help, Please, will give 20 points and brainiliest. URGENT!
Answer:
Step-by-step explanation:
b = 21 is the base, a is the height
area = 0.5ab = 210
ab = 420
a = 420/b = 420/21 = 20 ft
length of hypotenuse = √(a²+b²) = √(20²+21²) = √841 = 29 ft
hi everyone i know all the ansers but i wanna help people too 9x8 2x12